Department of Physics, University of Alberta, Edmonton, AB T6G 2E1, Canada.
Department of Physics, University of Alberta, Edmonton, AB T6G 2E1, Canada
Proc Natl Acad Sci U S A. 2019 Apr 23;116(17):8125-8130. doi: 10.1073/pnas.1816602116. Epub 2019 Apr 5.
Transition paths represent the parts of a reaction where the energy barrier separating products and reactants is crossed. They are essential to understanding reaction mechanisms, yet many of their properties remain unstudied. Here, we report measurements of the average shape of transition paths, studying the folding of DNA hairpins as a model system for folding reactions. Individual transition paths were detected in the folding trajectories of hairpins with different sequences held under tension in optical tweezers, and path shapes were computed by averaging all transitions in the time domain, 〈()〉, or by averaging transitions of a given duration in the extension domain, 〈(|)〉 Whereas 〈()〉 was close to straight, with only a subtle curvature, 〈(|)〉 had more pronounced curvature that fit well to theoretical expectations for the dominant transition path, returning diffusion coefficients similar to values obtained previously from independent methods. Simulations suggested that 〈()〉 provided a less reliable representation of the path shape than 〈(|)〉 , because it was far more sensitive to the effects of coupling the molecule to the experimental force probe. Intriguingly, the path shape variance was larger for some hairpins than others, indicating sequence-dependent changes in the diversity of transition paths reflective of differences in the character of the energy barriers, such as the width of the barrier saddle-point or the presence of parallel paths through multiple barriers between the folded and unfolded states. These studies of average path shapes point the way forward for probing the rich information contained in path shape fluctuations.
过渡路径表示反应物和产物之间的能量势垒被跨越的反应部分。它们对于理解反应机制至关重要，但它们的许多性质仍未被研究。在这里，我们报告了对过渡路径平均形状的测量结果，研究了 DNA 发夹折叠作为折叠反应的模型系统。在光学镊子中拉伸的具有不同序列的发夹的折叠轨迹中检测到了单个过渡路径，并通过在时域中平均所有过渡来计算路径形状，〈()〉，或通过在延伸域中平均给定持续时间的过渡来计算路径形状，〈(|)〉。虽然〈()〉接近于直线，只有细微的曲率，但〈(|)〉的曲率更为明显，与理论上对主要过渡路径的预期非常吻合，返回的扩散系数与先前从独立方法获得的值相似。模拟表明，〈()〉比〈(|)〉更能可靠地表示路径形状，因为它对分子与实验力探针耦合的影响更为敏感。有趣的是，对于某些发夹，路径形状的方差比其他发夹更大，这表明过渡路径的多样性存在序列依赖性，反映了能量势垒的特征差异，例如势垒鞍点的宽度或折叠态和未折叠态之间多个势垒的平行路径的存在。这些对平均路径形状的研究为探测路径形状波动中包含的丰富信息指明了方向。
